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1. Dispersion‐enhanced sequential batch sampling for adaptive contour estimation

   https://doi.org/10.1002/qre.3245  

   Che, Yiming; Müller, Juliane; Cheng, Changqing (February 2024, Quality and Reliability Engineering International)

   In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two‐dimensional four‐branch function, a four‐dimensional function with a disjoint contour of interest and a time‐delay dynamic system. 

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2. Epistemic Uncertainty Quantification in State-space LPV Model Identification Using Bayesian Neural Networks

   Bao, Yajie; Mohammadpour Velni, Javad; Shahbakhti, Mahdi (January 2020, IEEE control systems letters)

   This paper presents a variational Bayesian inference Neural Network (BNN) approach to quantify uncertainties in matrix function estimation for the state-space linear parameter-varying (LPV) model identification problem using only inputs/outputs data. The proposed method simultaneously estimates states and posteriors of matrix functions given data. In particular, states are estimated by reaching a consensus between an estimator based on past system trajectory and an estimator by recurrent equations of states; posteriors are approximated by minimizing the Kullback–Leibler (KL) divergence between the parameterized posterior distribution and the true posterior of the LPV model parameters. Furthermore, techniques such as transfer learning are explored in this work to reduce computational cost and prevent convergence failure of Bayesian inference. The proposed data-driven method is validated using experimental data for identification of a control-oriented reactivity controlled compression ignition (RCCI) engine model. 

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3. Novel Tool for Selecting Surrogate Modeling Techniques for Surface Approximation

   https://doi.org/10.1016/B978-0-323-88506-5.50071-1  

   Williams, B. Cremaschi (January 2021, Computer aided chemical engineering)

   Turkay, M. Aydin (Ed.)

   Surrogate models are used to map input data to output data when the actual relationship between the two is unknown or computationally expensive to evaluate for several applications, including surface approximation and surrogate-based optimization. Many techniques have been developed for surrogate modeling; however, a systematic method for selecting suitable techniques for an application remains an open challenge. This work compares the performance of eight surrogate modeling techniques for approximating a surface over a set of simulated data. Using the comparison results, we constructed a Random Forest based tool to recommend the appropriate surrogate modeling technique for a given dataset using attributes calculated only from the available input and output values. The tool identifies the appropriate surrogate modeling techniques for surface approximation with an accuracy of 87% and a precision of 86%. Using the tool for surrogate model form selection enables computational time savings by avoiding expensive trial-and-error selection methods. 

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4. Modeling sparse longitudinal data on Riemannian manifolds

   https://doi.org/10.1111/biom.13385  

   Dai, Xiongtao; Lin, Zhenhua; Müller, Hans‐Georg (October 2020, Biometrics)

   Abstract Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold‐valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state‐of‐the‐art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine‐invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database. 

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5. Surrogate Bayesian Networks for Approximating Evolutionary Games

   Hsiao, Vincent; Nau, Dana S; Dechter, Rina (May 2024, PMLR)

   Dasgupta, Sanjoy; Mandt, Stephan; Li, Yingzhen (Ed.)

   Spatial evolutionary games are used to model large systems of interacting agents. In earlier work, a method was developed using Bayesian Networks to approximate the population dynamics in these games. One advantage of that approach is that one can smoothly adjust the size of the network to get more accurate approximations. However, scaling the method up can be intractable if the number of strategies in the evolutionary game increases. In this paper, we propose a new method for computing more accurate approximations by using surrogate Bayesian Networks. Instead of doing inference on larger networks directly, we do it on a much smaller surrogate network extended with parameters that exploit the symmetry inherent to the domain. We learn the parameters on the surrogate network using KL-divergence as the loss function. We illustrate the value of this method empirically through a comparison on several evolutionary games. 

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